President Obama says that the demise of the government of prime minister Nouri al-Maliki justifies a more interventionist US role in Iraq. This is a big mistake. This response is based on the same faulty logic that helped precipitate this crisis: that the removal of an Iraqi strongman (Saddam Hussein in 2003, Nouri al-Maliki today) would somehow lead to a viable democratic state. Instead of ending the moral and strategic catastrophe unfolding across northern and western Iraq, an intensified US-led military effort could lead to big trouble for Washington and possibly allies, such as Australia.

The White House view, widely shared by foreign policy analysts, is that the authoritarian Maliki is the main obstacle to the creation of an inclusive government that would unify Iraq. If only the different Shia, Sunni and Kurdish sects could reconcile their differences, the argument goes, America would then be fighting for the good guys.

But this is foreign policy in service of Rodney King and his question during the LA Riots in 1992: “Can’t we all get along?” Alas, Iraqis can’t all get along, because the hatred, rivalries and vengefulness are so much part of Iraqi religious, sectarian and tribal animosities.

The genesis of Baghdad’s political problems was the decision to invade Iraq in March 2003. It was the invasion that allowed all those age-old ethnic and tribal tensions to resurface. During his eight-year tenure, Maliki has been more interested in seeking revenge against his political and sectarian rivals, especially the Sunni Arabs, than in building a nation. It is highly unlikely things will change in any post-Maliki era.

For generations, the Sunnis held a disproportionate share of power and resources, and at the same time brutally suppressed Shia and Kurds. With the “liberation” of Iraq, however, that imbalance came to an end.

In the post-Saddam era, the Shia have been the political winners; the Sunnis have been the losers. The Shia still fear Sunni rule and want payback for generations of mistreatment; and the Sunnis still lament their loss of power and want to be back on top again. As Vali Nasr, dean at the Paul Nitze School of Advanced International Studies in Washington, puts it: “Each [ethnic group] has a different vision of the past and a different dream for the future,” he argues. “There are still scores to settle.”

Meanwhile, the American people are in no mood to go abroad in search of new monsters to destroy. A June WSJ/NBC poll shows that 71% say the Iraq war was “not worth it.” And a Pew poll several months ago shows that a majority of war-weary Americans think the US “should mind its own business internationally.” To the extent that such views prevail, they are inimical to the kind of a Pax Americana that people like John McCain and Hillary Clinton are panting for.

All of this is why Washington and its allies, such as Australia, need to think clearly and perhaps coldly about any further military intervention. Limited air strikes to stop Islamic militants from advancing to Kurdish areas are one thing: it is justified to help defenceless people from being massacred by a bunch of pre-modern barbarians on the rampage. But an enhanced US-led military role is another thing altogether: among other things, it would reinforce perceptions among even moderate Sunnis that Washington is favouring the Shia, would unite Sunnis against other sects, and perhaps even boost support for the Islamic State. It would also aggravate relations with the US allies in the Persian Gulf that are opposed to any Shia leadership in Baghdad.

Ultimately, this is not America’s (or Australia’s) war to fight and win. Ironically, it’s other unpleasant actors in the region – Iran, Hezbollah and Assad’s Syria – that have a greater interest in stopping the Islamic State in their region.

The lesson of Iraq, as the Australian conservative Owen Harries warned before the invasion, is that democracy is not an export commodity to arbitrarily created and ethnically divided societies. It is an essentially do-it-yourself enterprise that requires special conditions and circumstances, which remain sorely lacking in Iraq.

Judging from his recent statements, perhaps even Barack Obama, a man who ran on a campaign that “nation building begins at home”, has not fully grasped that lesson. And if Australia’s leaders are foolish enough to follow the Americans in another misbegotten venture in Iraq, neither have we.